Italian Physical Society International School of Physics

“Enrico Fermi”

CP ViolationTopics to be covered

Lecture 11. Introduction• Why study CP violation?• Grand view - Sakharov's ideas2. Symmetries • Mechanics • Electrodynamics• Quantum mechanics　　　 time reversal operator　　　 anti-unitary operator

Lecture　２• Edm• Krammer’s degeneracy• Particle physics• How do you measure pion spin?• How do you show that pion is a pseudos

calar?• G-parity• C,P,T in particle physics

Lecture 3

3. K meson system

• τ-θ Puzzl• Weak interaction• CPT • Mixing ４． CP violation• Asymmetry in partial widths• Role of final state interaction• Hyperon decays• Watson's theorem

Lecture 4•Regeneration•Explain Eq. 7.8 and Fig 7,.1•Discovery of CP violation Cronin-Fitch experiment•Direct•indirect

• In this section, we refrain from deriving the expression for ε and ε' etc.

Lecture 5CP violation in B decays

Towards building the B factoryEPR paradox Experiments at the B factory without much about the KM formalism

Its goes back the basic question asked by man.Why do we exist?

13.7 billion years

270

2810 cm

4310Time(sec)

3410

Temp( )℃3010 2610

1m410 cmradius

1010protons and neutrons

1510

100Km

Light

elements

1310410

1 billion

years

Stars and m

ilky w

ay

5 billion years

Supernova and heavy

elements

We are here

100910

Nucleosythesis of

Helium

Black-body radiationThe universe is filled with 　３ °Ｋ　　（－２７０℃） photons

Generation of light elements

Expanding universeMeasuring the speed of expansion

universe

anti-universeTheory predicts universe and anti-universe

1. You can see Armstrong’s foot step. The moon is not made out of anti-matter

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

10-1 1 10 102 103

Rigidity (GV)

Ant

ihel

ium

/hel

ium

flux

ratio

He/He limit (95% C.L.)

Evenson (1972)

Evenson (1972)

Smoot et al. (1975)

Smoot et al. (1975)

Badhwar et al. (1978)

Aizu et al. (1961)

Buffington et al. (1981)

Golden et al. (1997)

Ormes et al. (1997) BESS-95

T. Saeki et al. (1998) BESS-93~95

J . Alcaraz et al. (1999) AMS01

BESS-1993~2000Preliminary

M. Sasaki (2000)BESS-93~98

BESS-Polar (2003, 20 days)

PAMELA (2002~, 3 years)

AMS02 (2004~, 3 years)

KEK/IPNS　 Yoshida

2.No primary anti-particle in cosmic rays BESS experiment KEK/IPNS

3.You see galaxy collisions but collisions of galaxy and anti-galaxy have been found

Really absent？

Alpha Matter SpectrometerSpace Shuttle NASA program

SEMINAR – EXPERIMENTS ON ANTIMATTER SEARCHES IN SPACE Battison

We have to understand how CP is violated in the fundamental theory

16

29

3

80

10 sec

10

270

200 /

10 ,

0 ,

t

r cm

T C

cm

p n

p n

Why there is no anti-universe

三田一郎　名古屋大学大学院　理学研究科

1. Anti-baryon has to disappear. So, there has to be baryon number violation

2. Only anti-baryon has to disappear. So, there has to be CP violation

3. Created asymmetry will be washed out if the universe is in equilibrium. So, baryon has to be created out of equilibrium.

X qe

X qe

®

®

88 80

88

10 10

10

N

N

= +

=

88 80 88

88 80 8810 10 1010 10 10

810

N NN N

+ --+ + +

-

=

=

These annihilationsProduce light

16

29

3

80

10 sec

10

270

200 /

10 ,

0 ,

t

r cm

T C

cm

p n

p n

GUT

God

CP

Proton Decay

Baryon number

STANDARD MODEL

Quark Mass

CP violation in K system

CP violation in K system

50-100%CP violationin B system

50-100%CP violationin B system

strings

The origin of quark massesThe origin of CP violation

So, let us go back to symmetries

Mirror image

x x

Time reversalt t

You can’t tell which is the original

The symmetry is imbedded in your brain

Newton’s Equation

2

2

d rF m

dt

Show that this equation is invariant under parity Show that this equation is invariant under time reversal

Maxwell Equation4

1 4

0

10

E

EB J

c t c

B

BE

c t

Parity

4

1 4

0

10

E

EB J

c t c

B

BE

c t

E E

B B

( )

F ma

F q E v B

Charge conjugation

4

1 4

0

10

E

EB J

c t c

B

BE

c t

E E

B B

J J

( )

F ma

F q E v B

Time Reversal

4

1 4

0

10

E

EB J

c t c

B

BE

c t

d d

dt dt

E E

B B

J J( )

F ma

F q E v B

Our cells are controlled by electrodynamics.Why don’t we get younger?

Symmetries and quantum mechanics

i iΩ

:

:

:

P r r

C e e

T t t

[H,Ω ]=0

1 1

| ; | ;

| ; | ;

| ; | ;

i t H tt

i t H tt

i t H tt

　 　 ψ and Ω ψ are both solutions to the Schorodinger Eq.

† †ψ ψ =ψ Ω Ω ψ Ω Ω =1So, you can’t tell the difference!

d

d

= -

=+

P x x

so we take 1

i

i

e

e

1

X x

P XP X

XP x PX x

x

xP

x

x

P x x

XP x xP x

2 -1 †P =1, P=P , P=P

1 1

| ; | ;

| ; | ;

| ; | ;

i t H tt

Pi P P t PHP P tt

i P t HP tt

(1) I f [P,H]=0

(2) i | , H | ,t

x H x = x H x

Show that

H( ) H( x)

then i ( , ) H(x)

x i | , H

( , )

:

| ,

t

t

P t P t

P t dy x y y t

t x t

P

x

xy y

y y

y y

¶=

¶¶

=¶

- -

= -

¶- = -

¶

ò

h

h

h

†

(3) ( ) is also solution to the Schordinger equation.

(1) P P

(

2) ( ) ( )

x x x x

Sho t

x

w h

x x

at

y

y y y y

y y± ± ± ±

±

±

±

- = = =±

- =±

&&

1(3) P is also a solition

2y y y

±é ù= ±ë û

( ) ( )x H y H x x y

2 2 2

22 2 2

p e eH A p p A A e

m mc mc

e e

A A

1CHC H

If charge of a particle is flipped, and the externalall fields are flipped, the motion is invariant.

1 1, , T x p T x p Ti T i

,x p i

Time reversal and quantum mechanics

* *

O=UK K is a complex conjugate operator

K α|a>+β|b>=α K|a>+β K|b>

†

|b>=O|b>

|a>=O|a>

|<a|b>|=|<a|O O|b>|=|<a|b>|

†<a|O O|b>=<a|b>

† *<a|O O|b>=<a|b>

†

† * † * †

K acts always to the lef t

[α <a|+β<b|]K =α <a|K + β <b|K

-1K =K2K =1

Ｔ＝Ｋ

-1 -1

i |ψ(t)>=H|ψ(t)>t

Ti T T|ψ(t)>=THT T|ψ(t)>t

-i T|ψ(t)>=HT|ψ(t)>t

T|ψ(t)>=|ψ(-t)>

ψ(-t) = dx' x' x' ψ(-t)

T ψ(t) =T dx' x' x' ψ(t) = dx' x' x' ψ(t) *

ò

ò ò

Show that x,p =i is consistent with time reversal.

Transf ormation of Schrodinger equation under T

Transf ormation of the wave f unction under T

ψ(x,-t)=ψ(x,t)*

i |ψ(-t)>=H|ψ(-t) > t

T ψ(t) =T dx' x' x' ψ(t) = dx' x' x' ψ(t) *ò ò

T (t) =T dy' y' y' (t) = dy' y' y' (t) *ff fò ò

†(t) T T ψ(t) = ' ' ' ( ) ' ' x' ψ(t) *dx dy y t y xff ò

†(t) T T ψ(t) =ψ(t) (t)ff

1. If T=K, from the definition of operator P, show that T-1PT=-P.

2. From the definition of J=rxP, show that T-

1JT=-J

' cos sin 0

' sin cos 0 around the z axis

' 0 0 0

' cos 0 sin

' 0 1 0 around th

' sin 0 cos

x x

y y

z z

x x

y y

z z

V V

V V

V V

V V

V V

V V

e y axis

' 1 0 0

' 0 cos sin around the x axis

' 0 sin cos

x x

y y

z z

V V

V V

V V

ziJe

Rotation operator

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 1 0 0 0 0z x y

i i

J i J i J

i i

1 if T=KTJ T J

x y

0 0 0 0 0 0 0

0 0 J 0 0 J 0 0 0

0 0 0 0 0 0 0z

i i

J i i

i i

x y

1 0 0 0 1 0 0 01 1

0 0 0 J 1 0 1 J 02 2

0 0 1 0 1 0

So we of ten use

0 0

:

z

i

J i i

i

But in quantum mechanics

fi rst question we ask:

what operator can we diagonalize

together with H.

2[ , ] 0H J

Then we have to change

p

T=K

ex yT i J K

[ , ] 0H J

[ , ]i j ijk kJ J i J